华罗庚先生首先得到了投入产出模型的崩溃定理并且研究了价格模型和带消费的模型. 陈木法先生首先将概率方法应用到投入产出模型并且研究了随机模型. 本文对基本模型的可逆性, 崩溃时和产品基数三个方面进行了推广, 并得到了崩溃时的上界估计. 同时推广了带消费模型的特征值定理的适用范围, 在一种特殊情形下证明了带消费模型的崩溃定理, 并且提出了一种新的带消费的模型.

L. Hua first obtained the collapse theorem of the input-output model and studied the model of price as well as model with consumption. M. Chen first applied the probability method to the input-output model and studied the stochastic model. For the basic model, invertibility, collapse time and product cardinal number are generalized and the upper bound estimation of collapse time is obtained. In the model with consumption, the application scope of the eigenvalue theorem is extended, collapse theorem for a special case is proved and a new model with consumption is presented.